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PROBABILITY

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Name: _____________________________________ Per. ____ Date: ______________
AP Statistics - Probability Review
Multiple Choice: Identify the choice that best completes the statement or answers the question.
____
1. In the table below, what are P(A and E) and P(C/E)?
D
E
Total
A
15
12
27
B
15
23
38
C
32
28
60
Total
62
63
125
a. 12/125, 28/125
b. 12/63, 28/60
c. 12/125, 28,63
____
d. 12/125, 28/60
e. 12/63, 28/63
2. For the tree diagram pictured below, what is P(B/X)?
a. 1/4
b. 5/17
c. 2/5
d. 1/3
e. 4/5
____
3. It turns out that 25 seniors at Lincoln High School took both the AP Statistics exam and the AP Spanish
Language exam. The mean score on the Stat exam for the 25 seniors was 2.4 with a standard deviation of
0.6, and the mean score on the Spanish Language exam was 2.65 with a standard deviation of 0.55. We want
to combine the scores into a single score. What are the correct mean and standard deviation of the combined
scores?
a. 5.05; 1.15
b. 5.05; 1.07
c. 5.05; 0.66
d. 5.05; 0.81
e. 5.05; standard deviation cannot be determined from this information
____
4. The GPAs of students who take the AP Statistics exam are approximately normally distributed with a mean of
3.4 and a standard deviation of 0.3. Using Table A, what is the probability that a student selected at random
from this group has a GPA lower than 3.0?
a. 0.0918
b. 0.4082
c. 0.9082
d. -0.0918
e. 0
____
5. The students’ GPAs in the previous problem were normally distributed with a mean GPA of 3.4 and a
standard deviation of 0.3. In order to qualify for the school honor society, a student must have a GPA in the
top 5% of all GPAs. Accurate to two decimal places, what is the minimum GPA James must have in order to
qualify for the honor society?
a. 3.95
b. 3.92
c. 3.75
d. 3.85
e. 3.89
____
6. Sixty percent of chocolate desserts ordered at a restaurant are ordered by women. Of these women, seventy
percent share their dessert. What is the probability that a randomly selected chocolate dessert was ordered by
a woman who will share it?
a. 0.13
b. 0.18
c. 0.42
d. 0.45
e. 0.70
____
7. The average weight of dogs that come to a certain vet’s office is 55.6 lbs, with standard deviation of 2.2 lbs.
If the weights are normally distributed, what percent of dogs weigh more than 60 lbs?
a. 66.8%
b. 47.2%
c. 33.4%
d. 15.9%
e. 2.28%
____
8. An intern goes to a coffee shop every day to buy four small coffees. Each cup contains a mean of 12 oz of
coffee, with a standard deviation of 1.2 oz. The cups holding the coffee each have a mean weight of 2 oz,
with a standard devaition of 0.1 oz. The intern carries the coffees in a carrier that has a mean weight of 8 oz,
with a standard deviation of 0.5 oz. What is the standard deviation of the weight of the carrier holding four
filled coffee cups?
a. 1.304 oz
b. 1.342 oz
c. 2.460 oz
d. 4.843 oz
e. 7.810 oz
____
9. At a certain college, ten percent of freshmen enter without a major declared. Of those who enter with a
major declared, twenty percent change it by the end of their second year. If the college admits 150
freshmen this year, how many will end their second year with the major they declared upon entry?
a. 12
b. 27
c. 108
d. 123
e. 147
____ 10. A math teacher and a history teacher each assigns her students a textbook for her class. A math text book has
an average weight of 8.00 lbs with a standard deviation of 0.41 lbs. A history textbook has an average
weight of 6.00 lbs with a standard deviation of 0.2 lbs.
What is the mean weight of both the textbooks?
a. 8 lbs
b. 14 lbs
c. 10 lbs
d. 6 lbs
e. 12 lbs
____ 11. The 2000 Census identified the ethnic breakdown of the state of California to be approximately as follows:
White: 46%, Latino: 32%, Asian: 11%, Black: 7%, and Other: 4%. Assuming that these are mutually
exclusive categories (this is not a realistic assumption), what is the probability that a randomly selected
person from the state of California is of Asian or Latino descent?
a. 46%
b. 32%
c. 11%
d. 43%
e. 3.5%
____ 12. You own an unusual die. Three faces are marked with the letter X, two faces with the letter Y, and one face
with the letter Z. What is the probability that at least one of the first two rolls is the letter Y?
a. 1/6
b. 2/3
c. 1/3
d. 5/9
e. 2/9
____ 13. You roll two six-sided dice. What is the probability that the sum is 6 given that one die shows a 4?
a. 2/12
b. 2/11
c. 11/36
d. 2/36
e. 12/36
____ 14. The following are the probability distributions of two random variables, X and Y:
X
3
5
P(X = x)
1/3
1/2
Y
1
3
P(Y = y)
1/8
3/8
7
1/6
4
?
5
3/16
If X and Y are independent, what is P(X = 5 and Y = 4)?
a. 5/16
b. 13/16
c. 5/32
d. 3/32
e. 3/16
____ 15. The following table gives the probabilities of various outcomes for a gambling game.
Outcome
Lose $1
Win $1
Win $2
Probability
0.6
0.25
0.15
What is the player’s expected return of a bet of $1?
a. $0.05
b. -$0.60
c. -$0.05
d. -$0.10
e. You can’t answer this question since this is not a complete probability distribution.
Short Answer
16. Find and
for the following discrete probability distribution:
X
2
3
4
P(X)
1/3
5/12
1/4
17. Given that P(A) = 0.6, P(B) = 0.3, and P(B/A) = 0.5
a) Find P(A and B) =
b) Find P(A or B) =
c) Are events A and B independent?
18. Consider a set of 9000 scores on a national test that is known to be normally distributed with a mean of 500
and a standard deviation of 90.
a) What is the probability that a randomly selected student has a score greater than 600?
b) How many scores are there between 450 and 600?
c) Rachel needs to be in the top 1% of the scores on this test to qualify for a scholarship. What is the
minimum score Rachel needs?
d) Ian scored in the 88th percentile. What was his actual score?
19. Harvey, Laura, and Gina take turns throwing darts at a target. Harvey hits the target 1/2 the time, Laura hits
it 1/3 of the time, and Gina hits the target 1/4 of the time. Given that somebody hit the target, what is the
probability that it was Laura?
20. Consider two discrete, independent, random variables X and Y with
Find
and
.
,
,
, and
.
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